The early ones did suffer from quite a bit of drift - mainly temperature dependent in my experience - but more modern ones are amazingly stable once you've set them up properly and isolated them as far as possible from any vibration.
I've considered using a MPU6050 for a novelty transmitter project with no sticks (except perhaps for the throttle). You would control the plane by simply rotating the whole transmitter slightly around its three axes for roll, pitch, and yaw control. Biggest problem would be if you accidentally flew back over your head, as turning around to face the plane would result in a sudden massive rudder control input
